Abstract [en]

Chain graphs are graphs with possibly directed and undirected edges, and no semidirected cycle. They have been extensively studied as a formalism to represent probabilistic independence models, because they can model symmetric and asymmetric relationships between random variables. This allows chain graphs to represent a wider range of systems than Bayesian networks. This in turn allows for a more correct representation of systems that may contain both causal and non-causal relationships between its variables, like for example biological systems. In this chapter we give an overview of how to use chain graphs and what research exists on them today. We also give examples on how chain graphs can be used to model advanced systems, that are not well understood, such as gene networks.

Abstract [en]

Probabilistic graphical models are today one of the most well used architectures for modelling and reasoning about knowledge with uncertainty. The most widely used subclass of these models is Bayesian networks that has found a wide range of applications both in industry and research. Bayesian networks do however have a major limitation which is that only asymmetric relationships, namely cause and eect relationships, can be modelled between its variables. A class of probabilistic graphical models that has tried to solve this shortcoming is chain graphs. It is achieved by including two types of edges in the models, representing both symmetric and asymmetric relationships between the connected variables. This allows for a wider range of independence models to be modelled. Depending on how the second edge is interpreted this has also given rise to dierent chain graph interpretations.

Although chain graphs were first presented in the late eighties the field has been relatively dormant and most research has been focused on Bayesian networks. This was until recently when chain graphs got renewed interest. The research on chain graphs has thereafter extended many of the ideas from Bayesian networks and in this thesis we study what this new surge of research has been focused on and what results have been achieved. Moreover we do also discuss what areas that we think are most important to focus on in further research.

Abstract [en]

Probabilistic graphical models are currently one of the most commonly used architectures for modelling and reasoning with uncertainty. The most widely used subclass of these models is directed acyclic graphs, also known as Bayesian networks, which are used in a wide range of applications both in research and industry. Directed acyclic graphs do, however, have a major limitation, which is that only asymmetric relationships, namely cause and effect relationships, can be modelled between their variables. A class of probabilistic graphical models that tries to address this shortcoming is chain graphs, which include two types of edges in the models representing both symmetric and asymmetric relationships between the variables. This allows for a wider range of independence models to be modelled and depending on how the second edge is interpreted, we also have different so-called chain graph interpretations.

Although chain graphs were first introduced in the late eighties, most research on probabilistic graphical models naturally started in the least complex subclasses, such as directed acyclic graphs and undirected graphs. The field of chain graphs has therefore been relatively dormant. However, due to the maturity of the research field of probabilistic graphical models and the rise of more data-driven approaches to system modelling, chain graphs have recently received renewed interest in research. In this thesis we provide an introduction to chain graphs where we incorporate the progress made in the field. More specifically, we study the three chain graph interpretations that exist in research in terms of their separation criteria, their possible parametrizations and the intuition behind their edges. In addition to this we also compare the expressivity of the interpretations in terms of representable independence models as well as propose new structure learning algorithms to learn chain graph models from data.